Hilaire Legros

On the excitation, detection and damping of core modes

Abstract We continue work on the possibility that internal oscillations in the Earths core might be detectable by a gravity meter at the surface. As a possible excitation mechanism we use earthquakes and for the damping we consider the contribution of anelasticity in both solid and liquid parts of the Earth. The calculation of the eigenfunctions is restricted in this paper to a non-rotating Earth model. We first review the spectrum of modes for degrees l up to 20 using a stably stratified fluid core based on the Preliminary Reference Earth Model (PREM) and compute the earthquake excitation and Q values using standard seismic theory. We then show that the effects of boundary rigidity and both Boussinesq and subseismic approximations in the core have little effect on the eigenfrequencies of the core modes. The rigid boundary core solutions are then extended into both the mantle and inner core by making use of a generalised internal load Love number approach. This method yields good approximations to the elastic eigenfunctions throughout the Earth, the agreement with full theory improving as the degree l increases. Thus we have confidence that this method can be extended successfully to models with rotation.

Core-mantle coupling and polar motion

Abstract We present the general expression for the topographic and electromagnetic torques acting at the core-mantle boundary (CMB) as a function of the outer core flow. Invoking angular momentum conservation of the Earth and of the core, we compute the perturbations in the rotation of the Earth, at the decade time-scale, resulting from this fluid motion, since 1900. Electromagnetic coupling is too weak to excite polar motion by two or three orders of magnitude. Although the pressure torque on a CMB topography computed by the authors involves some correlations between the temporal variation of the computed ω2-component of the polar motion and that observed, its amplitude is too weak by a factor of 10 and we have to conclude that it does not seem to be responsible for the decade variations of the polar motion.

Global Earth dynamics and induced gravity changes

We consider the elastogravitational deformation of an Earth model with a liquid outer core and a surficial fluid layer modeling the oceans or the atmosphere. The surface gravity changes caused by planetary-scale dynamical phenomena can be expressed in terms of generalized gravimetric factors. Each of these factors is related to a specific boundary condition (in normal or transverse traction, in potential and derivative) which has to be considered at the different interfaces (inner core-outer core, outer core-mantle, surface) according to the problem. We apply this formalism to express in a self-consistent and uniform manner the gravity disturbances due to various sources: tides, Earth rotation, loading process, inner and outer core dynamics, with special attention paid to possible resonance effects.

The search for weak harmonic signals in a spectrum with application to gravity data

Abstract When considering the search for discovery or amplitude estimation of a spectral line with a probabilistic approach, great attention must be paid to the meaning of each step. We give the probability law for the amplitude of a spectral peak in the presence of random noise appearing in a periodogram and discuss the effective probability of the existence of the corresponding wave. We find that the estimated amplitude of a spectral peak is biased and should be corrected when the signal-to-noise ratio is small. As a first application to gravity data, it results in a re-estimation of the gravimetric amplitude factors (delta factors) provided by least-squares tidal analysis. We also estimate the probability of observing a spectral line above a given level in the spectrum of a purely random noise. This allows us to compute for given spectrum the number of peaks expected to overcross the classical levels used in statistical analysis (like nσ, where σ is the standard deviation of the temporal noise distribution and n is an integer with typical values equal to 2 or 3). A specific application to real data is investigating the gravity spectrum derived from a 5 year record of the French superconducting gravimeter and we show that the predicted statistics are indeed in agreement with the observations. We also show the statistical consequence of using longer observing periods to obtain the spectral estimations. The problem of detecting translational motion of the Earths solid inner core (Slichter modes) in a gravity spectrum is analyzed and the probabilities of having a triplet of random peaks thresholding specific levels in a given frequency window are computed. We show that, in the case of a typical gravity spectrum (1 year of hourly data and a frequency window of 0.03 cycle h−1), the probability of having a random set of three peaks exceeding a level of 3 σ, is very high. This emphasizes the need for a very careful analysis of spectral lines before inferring the existence of a true physical signal.

Mass anomalies due to subducted slabs and simulations of plate motion since 200 My

Abstract In this paper we present a dynamic model where lithospheric plates are driven by the density heterogeneities of the upper mantle. We suppose that these heterogeneities are only related to the presence of subducted slabs. Paleogeographic reconstructions are used to infer the location of paleo-slabs at different ages of plate tectonic history. We choose to focus our simulations on three particular stages following the break-up of Pangea (180 Ma), following the Cretaceous reorganization (100 Ma), and following the Eocene reorganization (40 Ma) as well as on the present-day tectonics. We obtain a very good fit to the motions given by paleogeographic reconstitutions. The simulations clearly show that the forces issued from the gravity flow of subducted slabs are able to drive the plates in the right direction and that the major plate reorganizations are determined by the evolution of subduction zone geometry. However, the success of these models for predicting the stages of steady plate motion should not hide the fact that the real mechanism that abruptly reorganizes plate motions occurs on a time-scale that does not pertain to fluid dynamics and remains to be elucidated.

Tidal motions within the earth's fluid core: resonance process and possible variations

Abstract We intend to show how the amplitude of the tidally induced flow in the Earths fluid core is perturbed by the elastic yielding of the shell. Some possible variations of the resonance process as a function of the mantle mean rigidity, core geometry and size, and friction at the core-mantle boundary are investigated. The influence of the secular deceleration of the Earth is briefly considered.

Preliminary spectral analysis of the residual signal of a superconducting gravimeter for periods shorter than one day

We show for the first time an analysis of a 1.5 year data set from the superconducting gravimeter in Strasbourg. For periods between 7 and 24 h, a residual gravity signal is first generated by removal of the main tidal components by a standard least squares fit; this signal is then treated to suppress any remaining transient signals (de-spiking). At shorter periods, between 7 h and 10 min, a simple high-pass filter is applied before de-spiking. In both cases, the noise level is estimated in different frequency bands; spectra of the gravity residuals are shown. We also analysed by two different methods the local barometric pressure, which contains harmonic components of the S1 wave related to air pressure changes — driven by diurnal solar heating — superimposed on the frequency-dependent meteorological noise. After removal of the daily harmonics which are also present in the gravity residual spectrum, a few remaining spectral lines of possible geophysical interest are discussed.

Non-linear equations for the rotation of a viscoelastic planet taking into account the influence of a liquid core

Non-linear equations governing the temporal evolution of the vector of instantaneous rotation are developed for an Earth with a homogeneous mantle having a viscoelastic Maxwell rheology and with a homogeneous inviscid fluid core.This general theory is investigated using the angular momentum theorem applied to the coupled core-mantle system. It allows to study the influence upon the planetary rotation of a quasi-rigid rotational motion in the liquid core. It also enables to investigate the consequences of excitation sources (e.g. pressure), located at the core-mantle interface. Especially, the influence of viscoelastic variations in the inertia tensors resulting from the rotation itself or from various excitation sources are detailed with the help of a Love number formalism. The equations of the linear theory for an elastic Earth with a liquid core, and the non-linear theory for a viscous planet with a quasi-fluid behavior are shown to be particular cases of our generalized system of equations. Some planetological applications may be derived from the quasi-fluid approximation.

MAGNETIC FIELD AND ROTATIONAL EIGENFREQUENCIES

Abstract The theory of the rotation of the fluid core is modified in order to take into account the magnetic field within the core. Because of the conductivity of the lower mantle, there is a frictional magnetic torque which appears at the core–mantle boundary (CMB); the magnitude of this torque depends on the conductivity profile within the mantle and on the magnetic energy at the CMB. It perturbs the rotational eigenmodes involving a damping in the free core nutation (FCN) and in the Chandler wobble. The geostrophic pressure at the CMB acts on the bumps of this interface involving a topographic torque. Because of the geostrophic rigidification, this surface pressure field is advected by the core velocity, and consequently, the topography being fixed in a frame related to the mantle, it appears a restoring torque acting on the core. Such a torque perturbs the FCN and creates a slow new rotational eigenmode.

Core-mantle coupling and viscoelastic deformations

Abstract Writing the angular momentum theorem for the Earth and for its fluid core, we show that there are couplings between the core and the mantle induced by viscomagnetic torque, by external active torque, by topographic torque acting at the core-mantle boundary (CMB) but also by viscoelastic deformations of the CMB which may perturb the axial rotations of the Earth and of the core. We compute these deformations at the CMB induced by the Pleistocenic deglaciation. The time-dependence of inertia tensor perturbations, i.e. the rheology of the mantle, is very important in the calculation of the coupling. Taking into account the passive viscomagnetic torque of tangential traction acting at the CMB, we investigate, for different values and various temporal evolutions of the topographic torque, the perturbations in the rotations of the Earth and of the core induced by the deglaciation, by the constant torque of tidal friction and by the 18.6 year tidal potential. We show that, for these excitation sources, the existence of a constant topographic torque involves the core oscillating with respect to the mantle and thus forbids any large drift of the core with respect to the mantle. However, it seems theoretically possible to have an excitation source with enough energy which involves a shift of the core with respect to the mantle. If the pressure within the fluid core varies with time, the motion of the core with respect to the mantle could be drastically different.